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"Metro style apps are full screen apps tailored to your users' needs, tailored to the device they run on, tailored for touch interaction, and tailored to the Windows user interface. Windows helps you interact with your users, and your users interact with your app." from MSDN.

A Metro style app is an app built using HTML5 or XAML+(C#,VB or C++), on Microsoft's new APIs - in short, it's a an app-widget-kinda-thing. Note that this is cross-platform compatible (Windows 8 will support ARM with metro apps) and that standard x86 apps built the "old way" will still continue to work, but are not considered metro apps, nor are they cross-platform compatible. There is also an app store for metro apps.

Due to the lack of system APIs, these apps are fairly limited - think iOS style apps, where it's sandboxed. Metro apps also make use of the cloud more than ever for data storage, and are required to stay open (user should not quit a metro app) unless rebooted or via task manager.

Metro style application redesigns the Windows user interface (more focus on clean typography and less on UI chrome),have a full screen UI, introduced Flat colored “live tiles”(update user about the application and draw them into application) ,heaving touch-centric style, designed for multitasking(Snapped view, Filled view),can be packaged up and distributed via the “Windows Application store ” and can be deployed in multiple locals and languages.